The eye gouge, or eye poke is just an attack on a softer/vital tissue. It can be no less or more effective than a strike to a harder target like the mouth, or the liver. MMA has plenty of examples of strikers having successfully stopped grapplers with strikes.
Of course in those examples, the strikers knew how to protect a safe position, improve/change their position, and how not to get into a bad spot or even what a bad spot is. The karateka in the OP vid should have improve his position a little better or change to a safer spot before attempting the gouge/poke. Then maybe use the gouge/poke as distraction to further get back to a safer base. Then once there he can poke away.
The gouge/poke is not meant to be a dim mak move. When the karateka was under mount, he needs to escape, and pull guard. He can pull the grappler in closer and control him. Then he can really drive a finger in very deep.